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On the exact location of the non-trivial zeros of Riemann's zeta function

Juan Arias de Reyna, Jan van de Lune (2014)

Acta Arithmetica

We introduce the real valued real analytic function κ(t) implicitly defined by e 2 π i κ ( t ) = - e - 2 i ϑ ( t ) ( ζ ' ( 1 / 2 - i t ) ) / ( ζ ' ( 1 / 2 + i t ) ) (κ(0) = -1/2). By studying the equation κ(t) = n (without making any unproved hypotheses), we show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ’(s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it follows that the ordinate of the zero 1/2 + iγₙ of ζ(s) is the unique solution to the equation κ(t) = n.

On the existence of a fuzzy integral equation of Urysohn-Volterra type

Mohamed Abdalla Darwish (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We present an existence theorem for integral equations of Urysohn-Volterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.

On the extension and generation of set-valued mappings of bounded variation

V. V. Chistyakov, A. Rychlewicz (2002)

Studia Mathematica

We study set-valued mappings of bounded variation of one real variable. First we prove the existence of an extension of a metric space valued mapping from a subset of the reals to the whole set of reals with preservation of properties of the initial mapping: total variation, Lipschitz constant or absolute continuity. Then we show that a set-valued mapping of bounded variation defined on an arbitrary subset of the reals admits a regular selection of bounded variation. We introduce a notion of generated...

On the fixed points in an ω -limit set

Jack G. Ceder (1992)

Mathematica Bohemica

Let M and K be closed subsets of [0,1] with K a subset of the limit points of M . Necessary and sufficient conditions are found for the existence of a continuous function f : [ 0 , 1 ] → [ 0 , 1 ] such that M is an ω -limit set for f and K is the set of fixed points of f in M .

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